Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-01-22
Journal of Physics A Mathematical and Theoretical 40 (23/03/2007) 4057-4073
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
10.1088/1751-8113/40/15/001
The solutions of the one-dimensional homogeneous nonlinear Boltzmann equation are studied in the QE-limit (Quasi-Elastic; infinitesimal dissipation) by a combination of analytical and numerical techniques. Their behavior at large velocities differs qualitatively from that for higher dimensional systems. In our generic model, a dissipative fluid is maintained in a non-equilibrium steady state by a stochastic or deterministic driving force. The velocity distribution for stochastic driving is regular and for infinitesimal dissipation, has a stretched exponential tail, with an unusual stretching exponent $b_{QE} = 2b$, twice as large as the standard one for the corresponding $d$-dimensional system at finite dissipation. For deterministic driving the behavior is more subtle and displays singularities, such as multi-peaked velocity distribution functions. We classify the corresponding velocity distributions according to the nature and scaling behavior of such singularities.
Barrat Alain
Ernst Matthieu H.
Trizac Emmanuel
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